Details

sample22.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	5	7
1	7	6
done	7	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize5.0ms

Local error

Found 1 expressions with local error:

13.4b

(/ x (+ (* x x) 1.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

15.0ms

(/ x (+ (* x x) 1.0))

series91.0ms

Counts

1 → 3

Calls

1 calls:

91.0ms

(/ x (+ (* x x) 1.0))

simplify2.7s

Counts

34 → 34

Iterations

Useful iterations: 2 (128.0ms)

Iter	Nodes	Cost
0	76	444
1	173	384
2	462	350
3	1120	350
4	3306	350
done	5000	350

prune121.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (fma x x 1.0)))
0.0b	(/ (/ x (sqrt (fma x x 1.0))) (sqrt (+ (* x x) 1.0)))
13.3b	(sqrt (+ (* x x) 1.0))
13.3b	(sqrt (fma x x 1.0))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
161×	`add-sqr-sqrt`
158×	`add-cube-cbrt` `*-un-lft-identity`
150×	`sqrt-prod`
25×	`associate-/l*`
12×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-div` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `clear-num` `associate-/r/` `flip-+`
1×	`hypot-def` `associate-/l/`

Counts

4 → 253

Calls

4 calls:

13.0ms	(/ x (sqrt (fma x x 1.0)))
41.0ms	(/ (/ x (sqrt (fma x x 1.0))) (sqrt (+ (* x x) 1.0)))
13.0ms	(sqrt (+ (* x x) 1.0))
2.0ms	(sqrt (fma x x 1.0))

series578.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/ x (sqrt (fma x x 1.0)))
248.0ms	(/ (/ x (sqrt (fma x x 1.0))) (sqrt (+ (* x x) 1.0)))
50.0ms	(sqrt (+ (* x x) 1.0))
74.0ms	(sqrt (fma x x 1.0))

simplify3.0s

Counts

265 → 265

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	346	6421
1	771	5278
2	1698	4881
3	4828	4687
done	5000	4687

prune633.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

10.9b	(sqrt (fma 1.0 (- 1.0 (* x x)) (pow x 4)))
11.4b	(fma 1.0 (- 1.0 (* x x)) (pow x 4))
13.3b	(sqrt (fma x x 1.0))
19.2b	(/ (hypot (pow 1.0 3/2) (pow x 3)) (sqrt (fma 1.0 (- 1.0 (* x x)) (pow x 4))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `sqrt-undiv` `hypot-udef` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 82

Calls

4 calls:

3.0ms	(sqrt (fma 1.0 (- 1.0 (* x x)) (pow x 4)))
1.0ms	(fma 1.0 (- 1.0 (* x x)) (pow x 4))
3.0ms	(sqrt (fma x x 1.0))
12.0ms	(/ (hypot (pow 1.0 3/2) (pow x 3)) (sqrt (fma 1.0 (- 1.0 (* x x)) (pow x 4))))

series698.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sqrt (fma 1.0 (- 1.0 (* x x)) (pow x 4)))
51.0ms	(fma 1.0 (- 1.0 (* x x)) (pow x 4))
101.0ms	(sqrt (fma x x 1.0))
426.0ms	(/ (hypot (pow 1.0 3/2) (pow x 3)) (sqrt (fma 1.0 (- 1.0 (* x x)) (pow x 4))))

simplify1.5s

Counts

94 → 94

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	150	2013
1	292	1876
2	733	1752
3	2048	1746
done	5001	1741

prune599.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 x) (/ 1.0 (pow x 3)))
0.0b	(/ 1.0 (pow x 5))
0.4b	(/ 1.0 (pow x 3))
18.5b	(+ (/ 1.0 (pow x 5)) (- (/ 1 x) (/ 1.0 (pow x 3))))

rewrite573.0ms

Algorithm

rewrite-expression-head

Rules

1770×	`times-frac`
1242×	`add-sqr-sqrt`
1223×	`*-un-lft-identity`
1198×	`add-cube-cbrt`
1040×	`prod-diff`
522×	`associate-+r+`
270×	`unpow-prod-down`
249×	`cube-prod`
112×	`div-inv`
92×	`sqr-pow`
82×	`cube-mult` `unpow3`
25×	`fma-def`
19×	`associate-/r*`
15×	`difference-of-squares`
14×	`add-exp-log`
13×	`fma-neg`
11×	`add-log-exp`
8×	`add-cbrt-cube`
6×	`div-exp` `associate-/l*` `distribute-lft-out--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out`
3×	`frac-add`
2×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-exp` `clear-num` `sum-log` `frac-sub` `flip--`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 1249

Calls

4 calls:

78.0ms	(- (/ 1 x) (/ 1.0 (pow x 3)))
8.0ms	(/ 1.0 (pow x 5))
10.0ms	(/ 1.0 (pow x 3))
322.0ms	(+ (/ 1.0 (pow x 5)) (- (/ 1 x) (/ 1.0 (pow x 3))))

series264.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (/ 1 x) (/ 1.0 (pow x 3)))
67.0ms	(/ 1.0 (pow x 5))
52.0ms	(/ 1.0 (pow x 3))
63.0ms	(+ (/ 1.0 (pow x 5)) (- (/ 1 x) (/ 1.0 (pow x 3))))

simplify3.4s

Counts

1261 → 1261

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	1137	49036
1	2236	39328
2	4207	26383
done	5000	26381

prune1.6s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes38.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 24.1b

bsearch97.0ms

Steps

Iters	Range		Point
10	8.937283511995443e-05	28405617999702.24	405.25086270285146
6	-8.347711366351171e+18	-1.3895445609299136e+18	-7.878457258558738e+18

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	32	65
1	38	51
done	38	51

end0.0ms

sample606.0ms

Algorithm

intervals

Results

366.0ms

8000×

body

valid